Question 1128343
The minute hand goes around 60 times for the hour hand to go 1/12 of the way.
One way to look at it is by degrees.
At 1 pm, the minute hand is vertical, and the hour hand has gone 30 degrees around (1 pm spot)
The minute hand moves 6 degrees a minute
The hour hand is 30 degrees ahead and is moving 30 degrees/60 minutes or 1/2 degree minute
The minute hand has to catch up 30 degrees and is catching up at 6-1/2, or 5.5 degrees per minute
30/5.5=5.4545 minutes to catch up.
this is 60*5.4545 or 327.27 sec or 5m27s

This will be the same for each hour.  At 2 pm, they will coincide at 10m54s, and at 3 pm 15.81.818 or 15.81.82
minutes, which is 16m22s
They will coincide at 3:16.22

11 times the hands are together going around the clock
60/11=5.4545, and that is the time (+1 hour) in between the times the hands coincide.